The simple answer is to have use extraction rule that gets the **RANDOMURLSTRING** then change the URLs in the requests to be, for example, HTTPS://SITE/idp/{{TheRandomString}}/resumeSAML20/idp/startSSO.ping where TheRandomString is the context parameter that holds the extracted value. Note the doubled curly braces ({{ and }}) around the context parameter.

Suppose a value returned by the first redirection needs to be captured but a normal web test would redirect again and so the response is not seen by the extraction rules. In this case need to handle the redirect explicitly. Set the Follow redirects property of the initial request to false then add extraction rule(s) to gather the wanted values. Add a new request after the initial request and use the extracted values in it as necessary. It is possible to extract the entire redirected url and set the Url field to the extracted value.